Thermoplastic vulcanizates made by dynamic vulcanization techniques predominantly use a semicrystalline polyolefin continuous phase and a dispersed rubber phase consisting of a copolymer of isobutylene or ethylene/propylene diene (EPDM) polymer. The copolymer from isobutylene or EPDM is highly preferred among rubbers in general because of their ability to retain their properties after high temperature processing and aging. They are not blended with rubbers from conjugated dienes having substantial amounts of residual unsaturation. Copolymers of isobutylene have different cure rates than rubbers with substantial amounts of residual unsaturation. Further, copolymers of isobutylene are not completely miscible with these other rubbers.